A Toy-Model Study of the Grazing Collisions in the Kinetic Theory

Autor:	Shigeru Takata
Rok vydání:	2015
Předmět:	Physics Toy model Lorentz gas Lorentz transformation Grazing collisions Statistical and Nonlinear Physics Collision Boltzmann equation symbols.namesake Singularity Classical mechanics Regularization (physics) Boltzmann constant symbols Jump Kinetic theory Mathematical Physics
Zdroj:	Journal of Statistical Physics. 160:770-792
ISSN:	1572-9613 0022-4715
DOI:	10.1007/s10955-015-1259-0
Popis:	As a toy model study for the grazing collision effect in the Boltzmann equation, a spatially homogeneous problem for the two-dimensional Lorentz gas from the initial data with a jump discontinuity is investigated. The collision kernel of our model has the same angular singularity as the Boltzmann collision kernel. Thanks to the simplicity of the model, the jump propagation and its regularization are clearly seen, depending on whether the collision cross-section is finite or infinite. Three types of behavior are observed: a jump propagation, a jump propagation accompanied with a divergent derivative, and no jump propagation. For the model with a critical parameter, the switching from the second type to the last is observed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89d969f594395bdf0a54a8945f9a718c https://doi.org/10.1007/s10955-015-1259-0 Zobrazit plný text záznamu Plný text ve formátu PDF